Prudential Life Insurance Co. of America filed detailed plans with New Jersey regulators for converting from a policyholder-owned company to a publicly traded one, the latest in a string of longtime "mutual" insurers to seek to tap the stock market.

The company's move, expected for months, reflects a tough, fast-changing, financial-services world. The biggest U.S. life insurer by almost any measure when baby boomers were growing up, Prudential has lost some of its pre-eminence as publicly traded companies such as...